Block #87,601

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 12:52:12 AM · Difficulty 9.2718 · 6,710,255 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a614f3245d145fc6e9c60a4f07b9135e35d74a0cb741ab740508c04267159526

View on Chainz ↗

Height

#87,601

Difficulty

9.271761

Transactions

Size

207 B

Version

Bits

09459224

Nonce

173,506

Timestamp

7/29/2013, 12:52:12 AM

Confirmations

6,710,255

Mined by

⛏️ P2SHAR3ERsDPqSXEEk69413rtTXP1xfuc7v3x5

Merkle Root

d77f5ccdb5419c4734af303495807ab27dc7efba7de8d5069d15a1c1f3c2e7f1

Transactions (1)

Coinbased77f5ccdb5419c…15a1c1f3c2e7f1

1 in → 1 out11.6200 XPM109 B

AR3ERsDP…fuc7v3x5

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.

5.194 × 10¹¹²(113-digit number)

51946357591978202947…48050031064431661419

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

5.194 × 10¹¹²(113-digit number)

51946357591978202947…48050031064431661419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.194 × 10¹¹²(113-digit number)

51946357591978202947…48050031064431661421

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

1.038 × 10¹¹³(114-digit number)

10389271518395640589…96100062128863322839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.038 × 10¹¹³(114-digit number)

10389271518395640589…96100062128863322841

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

2.077 × 10¹¹³(114-digit number)

20778543036791281179…92200124257726645679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.077 × 10¹¹³(114-digit number)

20778543036791281179…92200124257726645681

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

4.155 × 10¹¹³(114-digit number)

41557086073582562358…84400248515453291359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.155 × 10¹¹³(114-digit number)

41557086073582562358…84400248515453291361

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

8.311 × 10¹¹³(114-digit number)

83114172147165124716…68800497030906582719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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