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Block #2,145,532

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/4/2017, 4:04:35 PM Β· Difficulty 10.8886 Β· 4,696,330 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b0bb8d4a4a4e9260e85460ec34c810a9b949b03bd66e029d3e2d6d8e988a1349
View on Chainz β†—

Height

#2,145,532

Difficulty

10.888577

Transactions

2

Size

2.55 KB

Version

2

Bits

0ae379c7

Nonce

378,347,543

Timestamp

6/4/2017, 4:04:35 PM

Confirmations

4,696,330

Mined by

⛏️ P2SHAVi2U7eDuJuLcnxaaAS6BEKSGexd5sM5Lb

Merkle Root

c3af206c1ecfafc5ec5edc1e5e42fba53d240750ef9d294b11b878f54da0fd27
Transactions (2)
Coinbased01740edcf8f8c…208bbdf909bc32
1 in β†’ 1 out8.4500 XPM110 B
AVi2U7eD…xd5sM5Lb
77fb4dda6a4651…a203d929f47c1f
16 in β†’ 1 out14.4573 XPM2.36 KB
AdYBqjH3…o3xpsUWT
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.

1.097 Γ— 10⁹⁴(95-digit number)
10975613929367287999…00138575997723541719
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
1.097 Γ— 10⁹⁴(95-digit number)
10975613929367287999…00138575997723541719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.097 Γ— 10⁹⁴(95-digit number)
10975613929367287999…00138575997723541721
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
2.195 Γ— 10⁹⁴(95-digit number)
21951227858734575999…00277151995447083439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.195 Γ— 10⁹⁴(95-digit number)
21951227858734575999…00277151995447083441
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
4.390 Γ— 10⁹⁴(95-digit number)
43902455717469151998…00554303990894166879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.390 Γ— 10⁹⁴(95-digit number)
43902455717469151998…00554303990894166881
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
8.780 Γ— 10⁹⁴(95-digit number)
87804911434938303997…01108607981788333759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.780 Γ— 10⁹⁴(95-digit number)
87804911434938303997…01108607981788333761
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
1.756 Γ— 10⁹⁡(96-digit number)
17560982286987660799…02217215963576667519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.756 Γ— 10⁹⁡(96-digit number)
17560982286987660799…02217215963576667521
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
3.512 Γ— 10⁹⁡(96-digit number)
35121964573975321599…04434431927153335039
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:57,979,273 XPMΒ·at block #6,841,861 Β· updates every 60s
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