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Block #152,871

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/6/2013, 3:01:02 PM Β· Difficulty 9.8629 Β· 6,674,051 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0892c230c9c617a33d90afae2f88681c1f2cd489e8834448d2df8ee2ab04472d
View on Chainz β†—

Height

#152,871

Difficulty

9.862932

Transactions

1

Size

203 B

Version

2

Bits

09dce923

Nonce

67,109,542

Timestamp

9/6/2013, 3:01:02 PM

Confirmations

6,674,051

Mined by

⛏️ P2SHAT5A2KL6kAm5Pa3anhC8W4LVscCT16n6i2

Merkle Root

ddae4ecaff6ac6c26439525836535fbe3ee446fbad2eefc2135e91f95a5c2dfc
Transactions (1)
Coinbaseddae4ecaff6ac6…5e91f95a5c2dfc
1 in β†’ 1 out10.2600 XPM112 B
AT5A2KL6…CT16n6i2
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.

2.713 Γ— 10⁹⁷(98-digit number)
27130042470159343331…39473568217084696639
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
2.713 Γ— 10⁹⁷(98-digit number)
27130042470159343331…39473568217084696639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.713 Γ— 10⁹⁷(98-digit number)
27130042470159343331…39473568217084696641
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
5.426 Γ— 10⁹⁷(98-digit number)
54260084940318686662…78947136434169393279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.426 Γ— 10⁹⁷(98-digit number)
54260084940318686662…78947136434169393281
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
1.085 Γ— 10⁹⁸(99-digit number)
10852016988063737332…57894272868338786559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.085 Γ— 10⁹⁸(99-digit number)
10852016988063737332…57894272868338786561
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
2.170 Γ— 10⁹⁸(99-digit number)
21704033976127474665…15788545736677573119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.170 Γ— 10⁹⁸(99-digit number)
21704033976127474665…15788545736677573121
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
4.340 Γ— 10⁹⁸(99-digit number)
43408067952254949330…31577091473355146239
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:57,859,547 XPMΒ·at block #6,826,921 Β· updates every 60s
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