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Block #2,781,287

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/6/2018, 5:46:48 AM Β· Difficulty 11.6503 Β· 4,063,151 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8bcdbacc0bfef3c2aa61e00f25d2ae3222351b2ca0f0ed32018716959344c20d
View on Chainz β†—

Height

#2,781,287

Difficulty

11.650288

Transactions

1

Size

202 B

Version

2

Bits

0ba67942

Nonce

586,666,277

Timestamp

8/6/2018, 5:46:48 AM

Confirmations

4,063,151

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

b34c0c63b081cb143818fb1af430cb5e784191716f76e7d7c775320b53a1ad58
Transactions (1)
Coinbaseb34c0c63b081cb…75320b53a1ad58
1 in β†’ 1 out7.3600 XPM110 B
AZtxQr2F…7grUWrUz
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.

1.068 Γ— 10⁹⁹(100-digit number)
10684251027088677998…94235417237133393919
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
1.068 Γ— 10⁹⁹(100-digit number)
10684251027088677998…94235417237133393919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.068 Γ— 10⁹⁹(100-digit number)
10684251027088677998…94235417237133393921
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
2.136 Γ— 10⁹⁹(100-digit number)
21368502054177355996…88470834474266787839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.136 Γ— 10⁹⁹(100-digit number)
21368502054177355996…88470834474266787841
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
4.273 Γ— 10⁹⁹(100-digit number)
42737004108354711993…76941668948533575679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.273 Γ— 10⁹⁹(100-digit number)
42737004108354711993…76941668948533575681
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
8.547 Γ— 10⁹⁹(100-digit number)
85474008216709423987…53883337897067151359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.547 Γ— 10⁹⁹(100-digit number)
85474008216709423987…53883337897067151361
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
1.709 Γ— 10¹⁰⁰(101-digit number)
17094801643341884797…07766675794134302719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.709 Γ— 10¹⁰⁰(101-digit number)
17094801643341884797…07766675794134302721
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
3.418 Γ— 10¹⁰⁰(101-digit number)
34189603286683769595…15533351588268605439
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:57,999,900 XPMΒ·at block #6,844,437 Β· updates every 60s
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