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Block #271,141

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/24/2013, 10:56:32 AM Β· Difficulty 9.9516 Β· 6,527,795 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
acc6bea022f84f22ccd007213c19f3f7a72497ae57c2b3476ab084c72eadbc31
View on Chainz β†—

Height

#271,141

Difficulty

9.951567

Transactions

1

Size

200 B

Version

2

Bits

09f399e8

Nonce

113,586

Timestamp

11/24/2013, 10:56:32 AM

Confirmations

6,527,795

Mined by

⛏️ P2SHAbz38twNnWn3z2rrYPRTzbKGWSVkCgPh1J

Merkle Root

5e5c6218e8d2e131c51b30f807bc9e929f5872f7d128dbbc8bb8e97b23869478
Transactions (1)
Coinbase5e5c6218e8d2e1…b8e97b23869478
1 in β†’ 1 out10.0800 XPM109 B
Abz38twN…VkCgPh1J
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.

1.126 Γ— 10⁹⁷(98-digit number)
11263052280028408219…60554857826435983359
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
1.126 Γ— 10⁹⁷(98-digit number)
11263052280028408219…60554857826435983359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.126 Γ— 10⁹⁷(98-digit number)
11263052280028408219…60554857826435983361
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
2.252 Γ— 10⁹⁷(98-digit number)
22526104560056816438…21109715652871966719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.252 Γ— 10⁹⁷(98-digit number)
22526104560056816438…21109715652871966721
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
4.505 Γ— 10⁹⁷(98-digit number)
45052209120113632877…42219431305743933439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.505 Γ— 10⁹⁷(98-digit number)
45052209120113632877…42219431305743933441
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
9.010 Γ— 10⁹⁷(98-digit number)
90104418240227265754…84438862611487866879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.010 Γ— 10⁹⁷(98-digit number)
90104418240227265754…84438862611487866881
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
1.802 Γ— 10⁹⁸(99-digit number)
18020883648045453150…68877725222975733759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.802 Γ— 10⁹⁸(99-digit number)
18020883648045453150…68877725222975733761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,635,523 XPMΒ·at block #6,798,935 Β· updates every 60s
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