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Block #1,193,525

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/14/2015, 12:02:01 AM Β· Difficulty 10.8507 Β· 5,633,197 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3f22cd0e601042e1d0d325c9d6743e65b7a7c399a025f9441a27107ee069b772
View on Chainz β†—

Height

#1,193,525

Difficulty

10.850697

Transactions

2

Size

3.03 KB

Version

2

Bits

0ad9c748

Nonce

172,479,250

Timestamp

8/14/2015, 12:02:01 AM

Confirmations

5,633,197

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

30aba1754ec38769b7dda4b36295d20def2e905358417ab9bc11b43910e55d61
Transactions (2)
Coinbasec962501913eba8…ae7b250739dcb1
1 in β†’ 1 out8.5300 XPM116 B
AJCEY9yy…tg97E6zm
f18808cc351d04…eabe3f60008d48
19 in β†’ 2 out230.8782 XPM2.83 KB
AXeUoDp5…X4bxpbncAJVeRHXf…C2yREH1f
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.

1.194 Γ— 10⁹⁷(98-digit number)
11944485498002218911…89978235005020047999
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
1.194 Γ— 10⁹⁷(98-digit number)
11944485498002218911…89978235005020047999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.194 Γ— 10⁹⁷(98-digit number)
11944485498002218911…89978235005020048001
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
2.388 Γ— 10⁹⁷(98-digit number)
23888970996004437823…79956470010040095999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.388 Γ— 10⁹⁷(98-digit number)
23888970996004437823…79956470010040096001
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
4.777 Γ— 10⁹⁷(98-digit number)
47777941992008875647…59912940020080191999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.777 Γ— 10⁹⁷(98-digit number)
47777941992008875647…59912940020080192001
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
9.555 Γ— 10⁹⁷(98-digit number)
95555883984017751295…19825880040160383999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.555 Γ— 10⁹⁷(98-digit number)
95555883984017751295…19825880040160384001
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
1.911 Γ— 10⁹⁸(99-digit number)
19111176796803550259…39651760080320767999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.911 Γ— 10⁹⁸(99-digit number)
19111176796803550259…39651760080320768001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.822 Γ— 10⁹⁸(99-digit number)
38222353593607100518…79303520160641535999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,857,930 XPMΒ·at block #6,826,721 Β· updates every 60s
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