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Block #1,371,649

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 3:33:53 PM Β· Difficulty 10.8108 Β· 5,468,614 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f77558829462e83e90229df07101bb4e71aaf44629629529e0b448c547957c8c
View on Chainz β†—

Height

#1,371,649

Difficulty

10.810801

Transactions

1

Size

200 B

Version

2

Bits

0acf90af

Nonce

37,114,993

Timestamp

12/16/2015, 3:33:53 PM

Confirmations

5,468,614

Mined by

⛏️ P2SHAVKe9TxS3eidzqrGFvPo4pZF6ocYpVKQ9h

Merkle Root

eb276bc5f3d30d747a885d52bca479e8c26cb78d2ced66dd840564eab673105b
Transactions (1)
Coinbaseeb276bc5f3d30d…0564eab673105b
1 in β†’ 1 out8.5400 XPM109 B
AVKe9TxS…cYpVKQ9h
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.

1.673 Γ— 10⁹⁢(97-digit number)
16734848446638147635…29057361358277989119
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
1.673 Γ— 10⁹⁢(97-digit number)
16734848446638147635…29057361358277989119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.673 Γ— 10⁹⁢(97-digit number)
16734848446638147635…29057361358277989121
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
3.346 Γ— 10⁹⁢(97-digit number)
33469696893276295270…58114722716555978239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.346 Γ— 10⁹⁢(97-digit number)
33469696893276295270…58114722716555978241
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
6.693 Γ— 10⁹⁢(97-digit number)
66939393786552590541…16229445433111956479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.693 Γ— 10⁹⁢(97-digit number)
66939393786552590541…16229445433111956481
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
1.338 Γ— 10⁹⁷(98-digit number)
13387878757310518108…32458890866223912959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.338 Γ— 10⁹⁷(98-digit number)
13387878757310518108…32458890866223912961
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
2.677 Γ— 10⁹⁷(98-digit number)
26775757514621036216…64917781732447825919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.677 Γ— 10⁹⁷(98-digit number)
26775757514621036216…64917781732447825921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,966,418 XPMΒ·at block #6,840,262 Β· updates every 60s
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