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Block #261,883

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/16/2013, 6:36:19 AM Β· Difficulty 9.9704 Β· 6,541,535 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3fc3168928dc61539f0b9b7de7215d47405b7934beea2a7b16919536e31e3445
View on Chainz β†—

Height

#261,883

Difficulty

9.970358

Transactions

1

Size

199 B

Version

2

Bits

09f86968

Nonce

249,542

Timestamp

11/16/2013, 6:36:19 AM

Confirmations

6,541,535

Mined by

⛏️ P2SHAXbpyooSXrgsDVAsu6AkhX5vgBbup7bQTH

Merkle Root

ec2a0be10b2b3e467c0392f6a6fba0f63a588db4af413b86342dc0b153d63d80
Transactions (1)
Coinbaseec2a0be10b2b3e…2dc0b153d63d80
1 in β†’ 1 out10.0400 XPM109 B
AXbpyooS…bup7bQTH
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.

3.978 Γ— 10⁹³(94-digit number)
39789426971469761836…41417552493834004999
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
3.978 Γ— 10⁹³(94-digit number)
39789426971469761836…41417552493834004999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.978 Γ— 10⁹³(94-digit number)
39789426971469761836…41417552493834005001
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
7.957 Γ— 10⁹³(94-digit number)
79578853942939523673…82835104987668009999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.957 Γ— 10⁹³(94-digit number)
79578853942939523673…82835104987668010001
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
1.591 Γ— 10⁹⁴(95-digit number)
15915770788587904734…65670209975336019999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.591 Γ— 10⁹⁴(95-digit number)
15915770788587904734…65670209975336020001
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
3.183 Γ— 10⁹⁴(95-digit number)
31831541577175809469…31340419950672039999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.183 Γ— 10⁹⁴(95-digit number)
31831541577175809469…31340419950672040001
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
6.366 Γ— 10⁹⁴(95-digit number)
63663083154351618938…62680839901344079999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.366 Γ— 10⁹⁴(95-digit number)
63663083154351618938…62680839901344080001
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:57,671,375 XPMΒ·at block #6,803,417 Β· updates every 60s
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