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Block #1,612,625

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2016, 5:08:39 PM Β· Difficulty 10.6022 Β· 5,229,206 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
83c147b171f5cd10717d1c821fed5b74fab8eb2c0e6771ade9caf0b34b1c3ac6
View on Chainz β†—

Height

#1,612,625

Difficulty

10.602203

Transactions

1

Size

199 B

Version

2

Bits

0a9a29f6

Nonce

295,853,153

Timestamp

6/3/2016, 5:08:39 PM

Confirmations

5,229,206

Mined by

⛏️ P2SHARDGXUxUcQsu3rSVRbQZabXvftjMWPjad4

Merkle Root

5bc67ffc50c9e111f2e3abec88278bb0aedbc802df86a58d627a0aa03fa046c2
Transactions (1)
Coinbase5bc67ffc50c9e1…7a0aa03fa046c2
1 in β†’ 1 out8.8800 XPM109 B
ARDGXUxU…jMWPjad4
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.

6.137 Γ— 10⁹³(94-digit number)
61376788378501334810…85005087064722485569
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
6.137 Γ— 10⁹³(94-digit number)
61376788378501334810…85005087064722485569
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.137 Γ— 10⁹³(94-digit number)
61376788378501334810…85005087064722485571
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
1.227 Γ— 10⁹⁴(95-digit number)
12275357675700266962…70010174129444971139
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.227 Γ— 10⁹⁴(95-digit number)
12275357675700266962…70010174129444971141
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
2.455 Γ— 10⁹⁴(95-digit number)
24550715351400533924…40020348258889942279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.455 Γ— 10⁹⁴(95-digit number)
24550715351400533924…40020348258889942281
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
4.910 Γ— 10⁹⁴(95-digit number)
49101430702801067848…80040696517779884559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.910 Γ— 10⁹⁴(95-digit number)
49101430702801067848…80040696517779884561
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
9.820 Γ— 10⁹⁴(95-digit number)
98202861405602135696…60081393035559769119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.820 Γ— 10⁹⁴(95-digit number)
98202861405602135696…60081393035559769121
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:57,979,022 XPMΒ·at block #6,841,830 Β· updates every 60s
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