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Block #68,713

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2013, 5:22:46 AM Β· Difficulty 8.9899 Β· 6,738,755 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4a98a94fa45de0c66f27016f5aaa1394b00694e746054ade121e54d238729d7b
View on Chainz β†—

Height

#68,713

Difficulty

8.989919

Transactions

1

Size

200 B

Version

2

Bits

08fd6b50

Nonce

35

Timestamp

7/20/2013, 5:22:46 AM

Confirmations

6,738,755

Mined by

⛏️ P2SHAcwNx5MsnsUPFJuWjka7veFuhA9LFGkjN9

Merkle Root

482ba1c2e31185e9a99a925f78313fbda02fe401231d1805bb71c0e72d5b5dc6
Transactions (1)
Coinbase482ba1c2e31185…71c0e72d5b5dc6
1 in β†’ 1 out12.3600 XPM109 B
AcwNx5Ms…9LFGkjN9
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.300 Γ— 10⁹⁷(98-digit number)
53002160234652774786…41075273075802557439
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.300 Γ— 10⁹⁷(98-digit number)
53002160234652774786…41075273075802557439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.300 Γ— 10⁹⁷(98-digit number)
53002160234652774786…41075273075802557441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.060 Γ— 10⁹⁸(99-digit number)
10600432046930554957…82150546151605114879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.060 Γ— 10⁹⁸(99-digit number)
10600432046930554957…82150546151605114881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.120 Γ— 10⁹⁸(99-digit number)
21200864093861109914…64301092303210229759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.120 Γ— 10⁹⁸(99-digit number)
21200864093861109914…64301092303210229761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.240 Γ— 10⁹⁸(99-digit number)
42401728187722219828…28602184606420459519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.240 Γ— 10⁹⁸(99-digit number)
42401728187722219828…28602184606420459521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,703,768 XPMΒ·at block #6,807,467 Β· updates every 60s
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