Block #72,410

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 11:58:42 PM · Difficulty 8.9940 · 6,733,644 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

42628a6b2482bbaceeb904fb1f8401e848dfc09fb4696e9ba2ed5075bae9a6b2

View on Chainz ↗

Height

#72,410

Difficulty

8.994047

Transactions

Size

1.35 KB

Version

Bits

08fe79dc

Nonce

Timestamp

7/20/2013, 11:58:42 PM

Confirmations

6,733,644

Mined by

⛏️ P2SHALD4vzJs4Zwqrn14ZxtLe9UeDdGRCXP6ri

Merkle Root

b9a1725ddbbb9f395aaca2a79533fb838ea69c88acea0c848db11853f5d7ffbe

Transactions (2)

Coinbase0c0929a205955b…8f5baec6f1e9a5

1 in → 1 out12.3600 XPM110 B

ALD4vzJs…GRCXP6ri

cd4103fa5989be…42619f4b6841ba

10 in → 1 out123.7500 XPM1.16 KB

AeFtCaAt…9CWGXQ3x

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.

7.985 × 10⁹⁹(100-digit number)

79859020398429945577…00309610128547435469

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

7.985 × 10⁹⁹(100-digit number)

79859020398429945577…00309610128547435469

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.985 × 10⁹⁹(100-digit number)

79859020398429945577…00309610128547435471

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

1.597 × 10¹⁰⁰(101-digit number)

15971804079685989115…00619220257094870939

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.597 × 10¹⁰⁰(101-digit number)

15971804079685989115…00619220257094870941

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

3.194 × 10¹⁰⁰(101-digit number)

31943608159371978231…01238440514189741879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.194 × 10¹⁰⁰(101-digit number)

31943608159371978231…01238440514189741881

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

6.388 × 10¹⁰⁰(101-digit number)

63887216318743956462…02476881028379483759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.388 × 10¹⁰⁰(101-digit number)

63887216318743956462…02476881028379483761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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