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Block #74,639

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 12:11:42 PM Β· Difficulty 8.9956 Β· 6,729,292 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7cd5d638d575569bcbbba3059085b3ff1c8017a8c834d0ffcc53e5ab022c2f9d
View on Chainz β†—

Height

#74,639

Difficulty

8.995633

Transactions

1

Size

200 B

Version

2

Bits

08fee1cd

Nonce

1,263

Timestamp

7/21/2013, 12:11:42 PM

Confirmations

6,729,292

Mined by

⛏️ P2SHANey87HKeHbF7P31ach44cVFqNMGUx5bYr

Merkle Root

d52bf31a27b602e7ffe33a1142c73a6a46453ca4dcd825acfd86aace366e1793
Transactions (1)
Coinbased52bf31a27b602…86aace366e1793
1 in β†’ 1 out12.3400 XPM110 B
ANey87HK…MGUx5bYr
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.

1.237 Γ— 10⁹⁴(95-digit number)
12372971455022308256…71421176813471643079
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
1.237 Γ— 10⁹⁴(95-digit number)
12372971455022308256…71421176813471643079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.237 Γ— 10⁹⁴(95-digit number)
12372971455022308256…71421176813471643081
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
2.474 Γ— 10⁹⁴(95-digit number)
24745942910044616513…42842353626943286159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.474 Γ— 10⁹⁴(95-digit number)
24745942910044616513…42842353626943286161
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
4.949 Γ— 10⁹⁴(95-digit number)
49491885820089233026…85684707253886572319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.949 Γ— 10⁹⁴(95-digit number)
49491885820089233026…85684707253886572321
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
9.898 Γ— 10⁹⁴(95-digit number)
98983771640178466053…71369414507773144639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.898 Γ— 10⁹⁴(95-digit number)
98983771640178466053…71369414507773144641
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:57,675,498 XPMΒ·at block #6,803,930 Β· updates every 60s
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