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Block #2,719,784

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/24/2018, 8:44:45 PM Β· Difficulty 11.6128 Β· 4,120,671 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ef4367cbecfaf164a69132b0af447e6df0a35071f9f57dc9d64ea57ed4e23f88
View on Chainz β†—

Height

#2,719,784

Difficulty

11.612799

Transactions

1

Size

202 B

Version

2

Bits

0b9ce063

Nonce

110,422,149

Timestamp

6/24/2018, 8:44:45 PM

Confirmations

4,120,671

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

1aaa4c8a1b7e87c580f06e3565b8fd824718def179bc6f93024f24eb157e4dc9
Transactions (1)
Coinbase1aaa4c8a1b7e87…4f24eb157e4dc9
1 in β†’ 1 out7.4000 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.

2.988 Γ— 10⁹⁸(99-digit number)
29880690594448216028…98563221121101004799
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
2.988 Γ— 10⁹⁸(99-digit number)
29880690594448216028…98563221121101004799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.988 Γ— 10⁹⁸(99-digit number)
29880690594448216028…98563221121101004801
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
5.976 Γ— 10⁹⁸(99-digit number)
59761381188896432057…97126442242202009599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.976 Γ— 10⁹⁸(99-digit number)
59761381188896432057…97126442242202009601
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
1.195 Γ— 10⁹⁹(100-digit number)
11952276237779286411…94252884484404019199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.195 Γ— 10⁹⁹(100-digit number)
11952276237779286411…94252884484404019201
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
2.390 Γ— 10⁹⁹(100-digit number)
23904552475558572823…88505768968808038399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.390 Γ— 10⁹⁹(100-digit number)
23904552475558572823…88505768968808038401
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
4.780 Γ— 10⁹⁹(100-digit number)
47809104951117145646…77011537937616076799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.780 Γ— 10⁹⁹(100-digit number)
47809104951117145646…77011537937616076801
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
9.561 Γ— 10⁹⁹(100-digit number)
95618209902234291292…54023075875232153599
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:57,967,971 XPMΒ·at block #6,840,454 Β· updates every 60s
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