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Block #417,741

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/24/2014, 9:14:42 AM Β· Difficulty 10.3923 Β· 6,398,459 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4fbe1d1daa0e2bda1bf330341181acff71f87b096d71a28753a1d155bea7c938
View on Chainz β†—

Height

#417,741

Difficulty

10.392270

Transactions

1

Size

206 B

Version

2

Bits

0a646bcc

Nonce

3,084

Timestamp

2/24/2014, 9:14:42 AM

Confirmations

6,398,459

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

0d7730482e39d6cc9e6c7dc8d36e89c4a683bb40806d641ddf090294b405febb
Transactions (1)
Coinbase0d7730482e39d6…090294b405febb
1 in β†’ 1 out9.2500 XPM116 B
AbwWkWZt…kawDhufa
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.

4.165 Γ— 10⁹⁡(96-digit number)
41659899545120825093…05451247814311654839
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
4.165 Γ— 10⁹⁡(96-digit number)
41659899545120825093…05451247814311654839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.165 Γ— 10⁹⁡(96-digit number)
41659899545120825093…05451247814311654841
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
8.331 Γ— 10⁹⁡(96-digit number)
83319799090241650187…10902495628623309679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.331 Γ— 10⁹⁡(96-digit number)
83319799090241650187…10902495628623309681
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
1.666 Γ— 10⁹⁢(97-digit number)
16663959818048330037…21804991257246619359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.666 Γ— 10⁹⁢(97-digit number)
16663959818048330037…21804991257246619361
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
3.332 Γ— 10⁹⁢(97-digit number)
33327919636096660075…43609982514493238719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.332 Γ— 10⁹⁢(97-digit number)
33327919636096660075…43609982514493238721
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
6.665 Γ— 10⁹⁢(97-digit number)
66655839272193320150…87219965028986477439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.665 Γ— 10⁹⁢(97-digit number)
66655839272193320150…87219965028986477441
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:57,773,726 XPMΒ·at block #6,816,199 Β· updates every 60s
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