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Block #1,169,904

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2015, 2:53:06 PM Β· Difficulty 10.9357 Β· 5,639,745 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
28722a9164b91037c0d9e7ffbfed259229fc7517e98925fddfbe15be226fdc7e
View on Chainz β†—

Height

#1,169,904

Difficulty

10.935655

Transactions

2

Size

6.34 KB

Version

2

Bits

0aef870f

Nonce

33,413,957

Timestamp

7/25/2015, 2:53:06 PM

Confirmations

5,639,745

Mined by

⛏️ P2SHAQ4nVYGKqYQSsCLERBBhoHdKETZ7cuvyYi

Merkle Root

0d00600af74ccd32e6364941f15ef225129d03a159d6ae347ddaac6a8b0899bf
Transactions (2)
Coinbase9b59b8bba9a7eb…7198e38064af03
1 in β†’ 1 out8.4200 XPM110 B
AQ4nVYGK…Z7cuvyYi
120d4e846dfe26…17b8ca55811505
42 in β†’ 2 out108.9900 XPM6.14 KB
AbUhqPwL…np5aet1ZAQHE5e6H…xDwU3vYU
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.013 Γ— 10⁹⁢(97-digit number)
10137138801728071171…51976420492955854079
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.013 Γ— 10⁹⁢(97-digit number)
10137138801728071171…51976420492955854079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.013 Γ— 10⁹⁢(97-digit number)
10137138801728071171…51976420492955854081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.027 Γ— 10⁹⁢(97-digit number)
20274277603456142343…03952840985911708159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.027 Γ— 10⁹⁢(97-digit number)
20274277603456142343…03952840985911708161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
4.054 Γ— 10⁹⁢(97-digit number)
40548555206912284686…07905681971823416319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.054 Γ— 10⁹⁢(97-digit number)
40548555206912284686…07905681971823416321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
8.109 Γ— 10⁹⁢(97-digit number)
81097110413824569373…15811363943646832639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.109 Γ— 10⁹⁢(97-digit number)
81097110413824569373…15811363943646832641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.621 Γ— 10⁹⁷(98-digit number)
16219422082764913874…31622727887293665279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.621 Γ— 10⁹⁷(98-digit number)
16219422082764913874…31622727887293665281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.243 Γ— 10⁹⁷(98-digit number)
32438844165529827749…63245455774587330559
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,721,272 XPMΒ·at block #6,809,648 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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