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Block #1,612,933

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2016, 10:22:54 PM Β· Difficulty 10.6016 Β· 5,229,216 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
089f14ffa14f85b8fa3fc93e6f22574f28aca7bad0f633982a8d301a1a14410a
View on Chainz β†—

Height

#1,612,933

Difficulty

10.601603

Transactions

1

Size

199 B

Version

2

Bits

0a9a02a3

Nonce

1,349,129,703

Timestamp

6/3/2016, 10:22:54 PM

Confirmations

5,229,216

Mined by

⛏️ P2SHAXZYtNBBwpD5KQxUc8xV6Nt3kufhvs1wdx

Merkle Root

343ea226e50f1ae8eb71236cc0d1de654f879b727226e3addeac143c94f7f237
Transactions (1)
Coinbase343ea226e50f1a…ac143c94f7f237
1 in β†’ 1 out8.8800 XPM109 B
AXZYtNBB…fhvs1wdx
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.

1.366 Γ— 10⁹⁴(95-digit number)
13669338627414482587…02909540982559754519
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
1.366 Γ— 10⁹⁴(95-digit number)
13669338627414482587…02909540982559754519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.366 Γ— 10⁹⁴(95-digit number)
13669338627414482587…02909540982559754521
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
2.733 Γ— 10⁹⁴(95-digit number)
27338677254828965174…05819081965119509039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.733 Γ— 10⁹⁴(95-digit number)
27338677254828965174…05819081965119509041
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
5.467 Γ— 10⁹⁴(95-digit number)
54677354509657930348…11638163930239018079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.467 Γ— 10⁹⁴(95-digit number)
54677354509657930348…11638163930239018081
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
1.093 Γ— 10⁹⁡(96-digit number)
10935470901931586069…23276327860478036159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.093 Γ— 10⁹⁡(96-digit number)
10935470901931586069…23276327860478036161
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
2.187 Γ— 10⁹⁡(96-digit number)
21870941803863172139…46552655720956072319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.187 Γ— 10⁹⁡(96-digit number)
21870941803863172139…46552655720956072321
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:57,981,581 XPMΒ·at block #6,842,148 Β· updates every 60s
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