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Block #1,281,900

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/14/2015, 3:43:41 PM Β· Difficulty 10.8404 Β· 5,520,653 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4b1d43867bec98c30a1620f0c26c1e976df90e3204d585788eb81808f976ca56
View on Chainz β†—

Height

#1,281,900

Difficulty

10.840395

Transactions

1

Size

200 B

Version

2

Bits

0ad7241f

Nonce

176,391,028

Timestamp

10/14/2015, 3:43:41 PM

Confirmations

5,520,653

Mined by

⛏️ P2SHAK8UW42P2DaSNhiZkzAf49b9n91RZvisiZ

Merkle Root

bd43b36e20d5b52c0e6196fb3f5d48bdfd68f68f78abed92924e4bda88604cc5
Transactions (1)
Coinbasebd43b36e20d5b5…4e4bda88604cc5
1 in β†’ 1 out8.5000 XPM109 B
AK8UW42P…1RZvisiZ
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.

1.569 Γ— 10⁹⁢(97-digit number)
15698852024950719905…64567599058134466559
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
1.569 Γ— 10⁹⁢(97-digit number)
15698852024950719905…64567599058134466559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.569 Γ— 10⁹⁢(97-digit number)
15698852024950719905…64567599058134466561
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
3.139 Γ— 10⁹⁢(97-digit number)
31397704049901439810…29135198116268933119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.139 Γ— 10⁹⁢(97-digit number)
31397704049901439810…29135198116268933121
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
6.279 Γ— 10⁹⁢(97-digit number)
62795408099802879620…58270396232537866239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.279 Γ— 10⁹⁢(97-digit number)
62795408099802879620…58270396232537866241
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
1.255 Γ— 10⁹⁷(98-digit number)
12559081619960575924…16540792465075732479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.255 Γ— 10⁹⁷(98-digit number)
12559081619960575924…16540792465075732481
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
2.511 Γ— 10⁹⁷(98-digit number)
25118163239921151848…33081584930151464959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.511 Γ— 10⁹⁷(98-digit number)
25118163239921151848…33081584930151464961
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:57,664,437 XPMΒ·at block #6,802,552 Β· updates every 60s
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