Block #1,231,899

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/11/2015, 2:35:24 PM · Difficulty 10.7403 · 5,606,543 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

72cfc04624015045e88bcd9012249db27b35f37dfa2646abe53786dc68c0a1a5

View on Chainz ↗

Height

#1,231,899

Difficulty

10.740330

Transactions

Size

7.30 KB

Version

Bits

0abd864a

Nonce

166,408,155

Timestamp

9/11/2015, 2:35:24 PM

Confirmations

5,606,543

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

00f31a905ed95042e738f94896ab3b5ac5f58869d9bcebaca68b907d32021435

Transactions (3)

Coinbaseb707b00581a111…b8b232bc934498

1 in → 1 out8.7500 XPM116 B

AJCEY9yy…tg97E6zm

2eb931afd613dc…c49828d78b3ba8

47 in → 2 out320.1720 XPM6.87 KB

AM1VewCn…nhLz26Gt AQ8obrRF…hCezsXdr

26fe0a6e3ccf3c…62d7755963661a

1 in → 2 out1.9376 XPM226 B

AcGL7NJd…XoCUQk8m APQumjtH…kX6gGSxh

Prime Chain Origin

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

1.363 × 10⁹⁶(97-digit number)

13632159255181575794…49440373849181773119

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

1.363 × 10⁹⁶(97-digit number)

13632159255181575794…49440373849181773119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.363 × 10⁹⁶(97-digit number)

13632159255181575794…49440373849181773121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.726 × 10⁹⁶(97-digit number)

27264318510363151588…98880747698363546239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.726 × 10⁹⁶(97-digit number)

27264318510363151588…98880747698363546241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

5.452 × 10⁹⁶(97-digit number)

54528637020726303177…97761495396727092479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.452 × 10⁹⁶(97-digit number)

54528637020726303177…97761495396727092481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.090 × 10⁹⁷(98-digit number)

10905727404145260635…95522990793454184959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.090 × 10⁹⁷(98-digit number)

10905727404145260635…95522990793454184961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.181 × 10⁹⁷(98-digit number)

21811454808290521271…91045981586908369919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.181 × 10⁹⁷(98-digit number)

21811454808290521271…91045981586908369921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #1,231,899

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