Block #116,482

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/14/2013, 10:54:02 AM · Difficulty 9.7483 · 6,688,702 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

83dfb4860738f6d9a071fb92ce2eb9775a1360ca4bc0c40ebc920a010b1b6fe1

View on Chainz ↗

Height

#116,482

Difficulty

9.748295

Transactions

Size

734 B

Version

Bits

09bf903b

Nonce

49,109

Timestamp

8/14/2013, 10:54:02 AM

Confirmations

6,688,702

Mined by

⛏️ P2SHAHmvhRqWL5g4Fhy2RMfdSpypuGqgG5FwBR

Merkle Root

7cadc36e0fe1d1ee54a89fe42ff2a92366fd81231a73e2f014d55256657afb11

Transactions (3)

Coinbaseffd5b5e00a7ba3…d5f2eca28c1bce

1 in → 1 out10.5300 XPM109 B

AHmvhRqW…qgG5FwBR

2acbd50d6efbff…0519de98f60560

2 in → 2 out79.5900 XPM375 B

Ab7iXvjf…LnFwMDZn AQMWD7vT…r4iM6qiV

893cf2cf00da01…2f145210b5bea8

1 in → 1 out10.5700 XPM159 B

AdaPyCyZ…F83yVpEB

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.

9.480 × 10⁹⁵(96-digit number)

94800829671747383726…20811210234327982589

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

9.480 × 10⁹⁵(96-digit number)

94800829671747383726…20811210234327982589

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.480 × 10⁹⁵(96-digit number)

94800829671747383726…20811210234327982591

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

1.896 × 10⁹⁶(97-digit number)

18960165934349476745…41622420468655965179

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.896 × 10⁹⁶(97-digit number)

18960165934349476745…41622420468655965181

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

3.792 × 10⁹⁶(97-digit number)

37920331868698953490…83244840937311930359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.792 × 10⁹⁶(97-digit number)

37920331868698953490…83244840937311930361

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

7.584 × 10⁹⁶(97-digit number)

75840663737397906980…66489681874623860719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.584 × 10⁹⁶(97-digit number)

75840663737397906980…66489681874623860721

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

1.516 × 10⁹⁷(98-digit number)

15168132747479581396…32979363749247721439

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