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Block #39,304

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 1:16:41 PM Β· Difficulty 8.3024 Β· 6,777,577 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
db8ed75336eb49a6c88a66a9f09db5cf2ff88628df1aa4d1e46632b57d485a74
View on Chainz β†—

Height

#39,304

Difficulty

8.302416

Transactions

1

Size

201 B

Version

2

Bits

084d6b2a

Nonce

1,226

Timestamp

7/14/2013, 1:16:41 PM

Confirmations

6,777,577

Mined by

⛏️ P2SHAYCQsY6D71QgyTLoRYWSvnZpmJsFr8Cxp5

Merkle Root

0ec05e1c9413ee8790e29872cd1383f1480f8a279aa5d5261a1c1d145e0bb821
Transactions (1)
Coinbase0ec05e1c9413ee…1c1d145e0bb821
1 in β†’ 1 out14.4900 XPM109 B
AYCQsY6D…sFr8Cxp5
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.

2.484 Γ— 10⁹⁸(99-digit number)
24846872630394893478…71558685014993183959
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
2.484 Γ— 10⁹⁸(99-digit number)
24846872630394893478…71558685014993183959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.484 Γ— 10⁹⁸(99-digit number)
24846872630394893478…71558685014993183961
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
4.969 Γ— 10⁹⁸(99-digit number)
49693745260789786957…43117370029986367919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.969 Γ— 10⁹⁸(99-digit number)
49693745260789786957…43117370029986367921
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
9.938 Γ— 10⁹⁸(99-digit number)
99387490521579573914…86234740059972735839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.938 Γ— 10⁹⁸(99-digit number)
99387490521579573914…86234740059972735841
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
1.987 Γ— 10⁹⁹(100-digit number)
19877498104315914782…72469480119945471679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.987 Γ— 10⁹⁹(100-digit number)
19877498104315914782…72469480119945471681
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:57,779,087 XPMΒ·at block #6,816,880 Β· updates every 60s
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