Block #136,923

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/27/2013, 12:21:52 PM · Difficulty 9.8186 · 6,656,065 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7919bc195228d4b30e858a2e6a230e5d3099672d62cdffb10102407c5a4f5bb7

View on Chainz ↗

Height

#136,923

Difficulty

9.818631

Transactions

Size

804 B

Version

Bits

09d191d3

Nonce

19,856

Timestamp

8/27/2013, 12:21:52 PM

Confirmations

6,656,065

Merkle Root

8e6ca8459dacde68e0bbecd2c0f3582ca52f93878a77e5a60aeff89c64a0ccbe

Transactions (3)

Coinbased4993f5d578788…c124953c581664

1 in → 1 out10.3800 XPM110 B

AR6ZWq7p…mL6WFwyj

cab66dce0ba301…a759c6e741f19a

2 in → 2 out11.2532 XPM376 B

AU6X5QGJ…85iEWzJo AWp2fnd9…a5YFUjPB

c10f06324f1a60…9938f5d3e91ed0

1 in → 2 out4.1404 XPM227 B

ANN8gjLH…8ToruqzW AdDbhwiP…qNdfGEZp

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.

8.621 × 10⁹⁵(96-digit number)

86216529235527865823…01348860051164717599

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

8.621 × 10⁹⁵(96-digit number)

86216529235527865823…01348860051164717599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.621 × 10⁹⁵(96-digit number)

86216529235527865823…01348860051164717601

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

1.724 × 10⁹⁶(97-digit number)

17243305847105573164…02697720102329435199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.724 × 10⁹⁶(97-digit number)

17243305847105573164…02697720102329435201

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

3.448 × 10⁹⁶(97-digit number)

34486611694211146329…05395440204658870399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.448 × 10⁹⁶(97-digit number)

34486611694211146329…05395440204658870401

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

6.897 × 10⁹⁶(97-digit number)

68973223388422292658…10790880409317740799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.897 × 10⁹⁶(97-digit number)

68973223388422292658…10790880409317740801

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

1.379 × 10⁹⁷(98-digit number)

13794644677684458531…21581760818635481599

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