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Block #3,088,807

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/11/2019, 8:41:23 PM Β· Difficulty 11.0401 Β· 3,749,157 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
538d983c3e53ba3ad60fddd4d07544d88fd94cfbaf849919c7feefc5439bbccc
View on Chainz β†—

Height

#3,088,807

Difficulty

11.040094

Transactions

2

Size

1.58 KB

Version

2

Bits

0b0a4399

Nonce

108,485,793

Timestamp

3/11/2019, 8:41:23 PM

Confirmations

3,749,157

Mined by

⛏️ 4AUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

7a00e74dab0ca0ce7c47bd7bc48bdd286475e05de61fa9ab92a2b61f4cda4726
Transactions (2)
Coinbased03f7fb93b0013…acc41e490dff99
1 in β†’ 1 out8.2200 XPM110 B
AUMQRepm…tAfKmdW1
d7547b364bec30…0967612ce2f600
9 in β†’ 2 out2570.5999 XPM1.38 KB
AZQgL5kt…6NE43uZsAafLKVR5…BYWsLQkE
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.

3.612 Γ— 10⁹⁴(95-digit number)
36126961916737518457…50821025385232819199
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
3.612 Γ— 10⁹⁴(95-digit number)
36126961916737518457…50821025385232819199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.612 Γ— 10⁹⁴(95-digit number)
36126961916737518457…50821025385232819201
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
7.225 Γ— 10⁹⁴(95-digit number)
72253923833475036915…01642050770465638399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.225 Γ— 10⁹⁴(95-digit number)
72253923833475036915…01642050770465638401
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
1.445 Γ— 10⁹⁡(96-digit number)
14450784766695007383…03284101540931276799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.445 Γ— 10⁹⁡(96-digit number)
14450784766695007383…03284101540931276801
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
2.890 Γ— 10⁹⁡(96-digit number)
28901569533390014766…06568203081862553599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.890 Γ— 10⁹⁡(96-digit number)
28901569533390014766…06568203081862553601
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
5.780 Γ— 10⁹⁡(96-digit number)
57803139066780029532…13136406163725107199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.780 Γ— 10⁹⁡(96-digit number)
57803139066780029532…13136406163725107201
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
1.156 Γ— 10⁹⁢(97-digit number)
11560627813356005906…26272812327450214399
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:57,948,061 XPMΒ·at block #6,837,963 Β· updates every 60s
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