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Block #2,142,284

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/2/2017, 7:20:22 PM Β· Difficulty 10.8752 Β· 4,699,894 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0d9423b09e2c96087a269de39cf7b8b9502c41b9b00644d9e25dad8a68924cf2
View on Chainz β†—

Height

#2,142,284

Difficulty

10.875187

Transactions

1

Size

200 B

Version

2

Bits

0ae00c46

Nonce

1,506,466,892

Timestamp

6/2/2017, 7:20:22 PM

Confirmations

4,699,894

Mined by

⛏️ P2SHARxmfu6fH94RtjSzxDAoQnoVvBXk7NcTxj

Merkle Root

c80285fed18a5b6324c567e57d22c027ba0487a8907aac7d423e6601b4276a6c
Transactions (1)
Coinbasec80285fed18a5b…3e6601b4276a6c
1 in β†’ 1 out8.4400 XPM110 B
ARxmfu6f…Xk7NcTxj
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.

4.442 Γ— 10⁹⁡(96-digit number)
44420812790578825358…70040555221052620799
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
4.442 Γ— 10⁹⁡(96-digit number)
44420812790578825358…70040555221052620799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.442 Γ— 10⁹⁡(96-digit number)
44420812790578825358…70040555221052620801
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
8.884 Γ— 10⁹⁡(96-digit number)
88841625581157650717…40081110442105241599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.884 Γ— 10⁹⁡(96-digit number)
88841625581157650717…40081110442105241601
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
1.776 Γ— 10⁹⁢(97-digit number)
17768325116231530143…80162220884210483199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.776 Γ— 10⁹⁢(97-digit number)
17768325116231530143…80162220884210483201
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
3.553 Γ— 10⁹⁢(97-digit number)
35536650232463060287…60324441768420966399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.553 Γ— 10⁹⁢(97-digit number)
35536650232463060287…60324441768420966401
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
7.107 Γ— 10⁹⁢(97-digit number)
71073300464926120574…20648883536841932799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.107 Γ— 10⁹⁢(97-digit number)
71073300464926120574…20648883536841932801
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:57,981,815 XPMΒ·at block #6,842,177 Β· updates every 60s
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