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Block #171,517

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/19/2013, 1:29:39 PM Β· Difficulty 9.8642 Β· 6,635,042 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1c743cf8221c7d8078699954c0b12100278e5df348314aecc8b6609f52d8a54c
View on Chainz β†—

Height

#171,517

Difficulty

9.864231

Transactions

2

Size

424 B

Version

2

Bits

09dd3e37

Nonce

6,995

Timestamp

9/19/2013, 1:29:39 PM

Confirmations

6,635,042

Mined by

⛏️ P2SHARBvr1evuYzdjmXQBMTxCmA4hCNg7YPkPH

Merkle Root

d965f767798bbad484f733b58155b75e5745deac03c31bb7c659a21c02774153
Transactions (2)
Coinbase4bc9568837793c…620dedd0f88383
1 in β†’ 1 out10.2700 XPM109 B
ARBvr1ev…Ng7YPkPH
49151e85d824b1…24710e2240108e
1 in β†’ 2 out10.2400 XPM226 B
AcC6uT9B…gu1qVBppANjE4rRU…gZ9FpSTJ
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.

4.210 Γ— 10⁹²(93-digit number)
42103932446473450128…64454014778132607869
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
4.210 Γ— 10⁹²(93-digit number)
42103932446473450128…64454014778132607869
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.210 Γ— 10⁹²(93-digit number)
42103932446473450128…64454014778132607871
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
8.420 Γ— 10⁹²(93-digit number)
84207864892946900257…28908029556265215739
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.420 Γ— 10⁹²(93-digit number)
84207864892946900257…28908029556265215741
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
1.684 Γ— 10⁹³(94-digit number)
16841572978589380051…57816059112530431479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.684 Γ— 10⁹³(94-digit number)
16841572978589380051…57816059112530431481
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
3.368 Γ— 10⁹³(94-digit number)
33683145957178760103…15632118225060862959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.368 Γ— 10⁹³(94-digit number)
33683145957178760103…15632118225060862961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
6.736 Γ— 10⁹³(94-digit number)
67366291914357520206…31264236450121725919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,696,568 XPMΒ·at block #6,806,558 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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