Block #81,154

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 2:15:21 PM · Difficulty 9.2641 · 6,729,881 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0e9c17ec58998426f08dc8bf1568894136e42ffcd5900b21b282fd9a4fc74f3

View on Chainz ↗

Height

#81,154

Difficulty

9.264132

Transactions

Size

1.08 KB

Version

Bits

09439e24

Nonce

118,305

Timestamp

7/24/2013, 2:15:21 PM

Confirmations

6,729,881

Mined by

⛏️ P2SHAb21X67T5DQr4ovUU5fP661vRC7Swyycai

Merkle Root

2d600fdc9e60598409130e0d86bfa1a7bff7d96f0ec6fcb5c872d73c2bbfa65d

Transactions (3)

Coinbaseb60528df23d13c…10e1194ad95340

1 in → 1 out11.6600 XPM109 B

Ab21X67T…7Swyycai

9425b877f96b87…a115241501abea

2 in → 2 out48.8862 XPM376 B

AGPUQxVR…vRGKX1tL AR7akR6p…4mV7ALHt

dbc03e04718a8d…f649be14c7dcdd

3 in → 2 out32.2040 XPM524 B

ANkHsWm5…QYcNQ2pF AJ747jiz…AGaH9UGG

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.

1.410 × 10¹⁰⁷(108-digit number)

14102438232768084469…92170836526440280719

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

1.410 × 10¹⁰⁷(108-digit number)

14102438232768084469…92170836526440280719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.410 × 10¹⁰⁷(108-digit number)

14102438232768084469…92170836526440280721

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

2.820 × 10¹⁰⁷(108-digit number)

28204876465536168939…84341673052880561439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.820 × 10¹⁰⁷(108-digit number)

28204876465536168939…84341673052880561441

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

5.640 × 10¹⁰⁷(108-digit number)

56409752931072337878…68683346105761122879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.640 × 10¹⁰⁷(108-digit number)

56409752931072337878…68683346105761122881

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

1.128 × 10¹⁰⁸(109-digit number)

11281950586214467575…37366692211522245759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.128 × 10¹⁰⁸(109-digit number)

11281950586214467575…37366692211522245761

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

2.256 × 10¹⁰⁸(109-digit number)

22563901172428935151…74733384423044491519

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 #81,154

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