Block #61,785

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 3:21:57 PM · Difficulty 8.9743 · 6,728,155 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eff8f21dd6895be0eb6487f9ad8dc19533cea73851b4c2b7d210302fdceb3544

View on Chainz ↗

Height

#61,785

Difficulty

8.974303

Transactions

Size

200 B

Version

Bits

08f96be4

Nonce

895

Timestamp

7/18/2013, 3:21:57 PM

Confirmations

6,728,155

Merkle Root

7f97f0f137bd6190f76a13776f45e3eaa190275e9fa4882d6a16e29d577b5d35

Transactions (1)

Coinbase7f97f0f137bd61…16e29d577b5d35

1 in → 1 out12.4000 XPM110 B

AK1JUKWL…oPR4rN5o

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.

1.267 × 10⁹⁵(96-digit number)

12675960410624695548…24561619652653960079

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

1.267 × 10⁹⁵(96-digit number)

12675960410624695548…24561619652653960079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.267 × 10⁹⁵(96-digit number)

12675960410624695548…24561619652653960081

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

2.535 × 10⁹⁵(96-digit number)

25351920821249391096…49123239305307920159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.535 × 10⁹⁵(96-digit number)

25351920821249391096…49123239305307920161

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

5.070 × 10⁹⁵(96-digit number)

50703841642498782193…98246478610615840319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.070 × 10⁹⁵(96-digit number)

50703841642498782193…98246478610615840321

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

1.014 × 10⁹⁶(97-digit number)

10140768328499756438…96492957221231680639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.014 × 10⁹⁶(97-digit number)

10140768328499756438…96492957221231680641

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

2.028 × 10⁹⁶(97-digit number)

20281536656999512877…92985914442463361279

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