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Block #1,612,615

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2016, 4:57:27 PM Β· Difficulty 10.6020 Β· 5,229,816 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
39d8f85ae1a731aec4177b9200ed5c4bdec270e814afe226da6873947e1d222b
View on Chainz β†—

Height

#1,612,615

Difficulty

10.602025

Transactions

1

Size

199 B

Version

2

Bits

0a9a1e4c

Nonce

134,195,244

Timestamp

6/3/2016, 4:57:27 PM

Confirmations

5,229,816

Mined by

⛏️ P2SHAXBHzwwgXMa9CLGZA9VuktkRVgFcWAPcY7

Merkle Root

d5a10465c7105cf598f8b94286db9a13d02ddb69fe9b0423f36ab77420cd6d03
Transactions (1)
Coinbased5a10465c7105c…6ab77420cd6d03
1 in β†’ 1 out8.8800 XPM109 B
AXBHzwwg…FcWAPcY7
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.

3.722 Γ— 10⁹³(94-digit number)
37224340135395311172…99868441958824115799
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
3.722 Γ— 10⁹³(94-digit number)
37224340135395311172…99868441958824115799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.722 Γ— 10⁹³(94-digit number)
37224340135395311172…99868441958824115801
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
7.444 Γ— 10⁹³(94-digit number)
74448680270790622344…99736883917648231599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.444 Γ— 10⁹³(94-digit number)
74448680270790622344…99736883917648231601
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
1.488 Γ— 10⁹⁴(95-digit number)
14889736054158124468…99473767835296463199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.488 Γ— 10⁹⁴(95-digit number)
14889736054158124468…99473767835296463201
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
2.977 Γ— 10⁹⁴(95-digit number)
29779472108316248937…98947535670592926399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.977 Γ— 10⁹⁴(95-digit number)
29779472108316248937…98947535670592926401
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
5.955 Γ— 10⁹⁴(95-digit number)
59558944216632497875…97895071341185852799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.955 Γ— 10⁹⁴(95-digit number)
59558944216632497875…97895071341185852801
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:57,983,863 XPMΒ·at block #6,842,430 Β· updates every 60s
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