Block #708,505

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/5/2014, 5:33:19 PM · Difficulty 10.9575 · 6,085,551 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a96be43d8cb591603a424675c54766f2f6d3877231603e311f6ff7affbf81ef

View on Chainz ↗

Height

#708,505

Difficulty

10.957520

Transactions

Size

700 B

Version

Bits

0af52007

Nonce

33,012

Timestamp

9/5/2014, 5:33:19 PM

Confirmations

6,085,551

Merkle Root

27a78846e0f13aa5f9c849cc55e9dbf93ad3b9612adde7a32f726e5cb8bf50f5

Transactions (1)

Coinbase27a78846e0f13a…726e5cb8bf50f5

1 in → 16 out8.3200 XPM607 B

AJzWx2VD…j4ZSMit5 APfZjrNu…Wvzt6AFp Ac5sZcdP…kzV4eckG AebWhrRm…K61Qrkws AHH8JjCP…zqhsmuVM

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.

8.084 × 10¹⁰²(103-digit number)

80844668288580943230…13365993306293844319

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

8.084 × 10¹⁰²(103-digit number)

80844668288580943230…13365993306293844319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.084 × 10¹⁰²(103-digit number)

80844668288580943230…13365993306293844321

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

1.616 × 10¹⁰³(104-digit number)

16168933657716188646…26731986612587688639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.616 × 10¹⁰³(104-digit number)

16168933657716188646…26731986612587688641

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

3.233 × 10¹⁰³(104-digit number)

32337867315432377292…53463973225175377279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.233 × 10¹⁰³(104-digit number)

32337867315432377292…53463973225175377281

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

6.467 × 10¹⁰³(104-digit number)

64675734630864754584…06927946450350754559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.467 × 10¹⁰³(104-digit number)

64675734630864754584…06927946450350754561

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

1.293 × 10¹⁰⁴(105-digit number)

12935146926172950916…13855892900701509119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.293 × 10¹⁰⁴(105-digit number)

12935146926172950916…13855892900701509121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.587 × 10¹⁰⁴(105-digit number)

25870293852345901833…27711785801403018239

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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