Block #136,988

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/27/2013, 1:21:28 PM · Difficulty 9.8188 · 6,672,673 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

847eeb87dd654e7649637d5783c3634ad5562f95a6d2d4b4833aa99e4ea6fe69

View on Chainz ↗

Height

#136,988

Difficulty

9.818834

Transactions

Size

1014 B

Version

Bits

09d19f1d

Nonce

158,069

Timestamp

8/27/2013, 1:21:28 PM

Confirmations

6,672,673

Mined by

⛏️ P2SHAJqiY272sv6qFjfTUSpa8TDxWEamFP7A5J

Merkle Root

d119cb45c7a9e293c0a0f3f567dc149e29ea9c0a61d0ee55c1996698e8bfa070

Transactions (2)

Coinbasee8ec3bd0265f8f…dff0449bd3e324

1 in → 1 out10.3700 XPM109 B

AJqiY272…amFP7A5J

85d09ad98cdc3c…124f50cdb45846

5 in → 2 out267.4162 XPM817 B

AQXTmxq8…dFFndScH AaCbwZog…iTxhrfuA

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.

8.955 × 10⁹⁰(91-digit number)

89555816385378518716…44110995798381410399

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

8.955 × 10⁹⁰(91-digit number)

89555816385378518716…44110995798381410399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.955 × 10⁹⁰(91-digit number)

89555816385378518716…44110995798381410401

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

1.791 × 10⁹¹(92-digit number)

17911163277075703743…88221991596762820799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.791 × 10⁹¹(92-digit number)

17911163277075703743…88221991596762820801

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

3.582 × 10⁹¹(92-digit number)

35822326554151407486…76443983193525641599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.582 × 10⁹¹(92-digit number)

35822326554151407486…76443983193525641601

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

7.164 × 10⁹¹(92-digit number)

71644653108302814973…52887966387051283199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.164 × 10⁹¹(92-digit number)

71644653108302814973…52887966387051283201

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

1.432 × 10⁹²(93-digit number)

14328930621660562994…05775932774102566399

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

Block #136,988

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